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%I #15 Sep 09 2023 06:54:03
%S 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U 913008685901414400,21912208461633945600,525893003079214694400
%N Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167940/b167940.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,-276).
%F G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 276*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
%F From _G. C. Greubel_, Sep 08 2023: (Start)
%F G.f.: (1+t)*(1-t^16)/(1 - 24*t + 299*t^16 - 276*t^17).
%F a(n) = 23*Sum_{j=1..15} a(n-j) - 276*a(n-16). (End)
%t coxG[{16,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 05 2015 *)
%t CoefficientList[Series[(1+t)*(1-t^16)/(1-24*t+299*t^16-276*t^17), {t, 0, 50}], t] (* _G. C. Greubel_, Jul 01 2016; Sep 08 2023 *)
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) )); // _G. C. Greubel_, Sep 08 2023
%o (SageMath)
%o def A167940_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) ).list()
%o A167940_list(40) # _G. C. Greubel_, Sep 08 2023
%Y Cf. A154638, A169452, A170758.
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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